∫ x^2-2x+4cosθ-এর সমাধান করুন

$$\int x ^ { 2 } - 2 x + 4 \cos \theta$$

মূল্যায়ন করুন

$$4x\cos(\theta )+\frac{x^{3}}{3}-x^{2}+С$$

সমাধানের ধাপগুলো

Integrate the sum term by term.

$$\int x^{2}\mathrm{d}x+\int -2x\mathrm{d}x+\int 4\cos(\theta )\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int x^{2}\mathrm{d}x-2\int x\mathrm{d}x+4\int \cos(\theta )\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.

$$\frac{x^{3}}{3}-2\int x\mathrm{d}x+4\int \cos(\theta )\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. -2 কে \frac{x^{2}}{2} বার গুণ করুন।

$$\frac{x^{3}}{3}-x^{2}+4\int \cos(\theta )\mathrm{d}x$$

Find the integral of \cos(\theta ) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x^{3}}{3}-x^{2}+4\cos(\theta )x$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{x^{3}}{3}-x^{2}+4\cos(\theta )x+С$$

w.r.t. x পার্থক্য করুন

$$4\cos(\theta )+x^{2}-2x$$